Coherence Based Sufficient Condition for Support Recovery Using Generalized Orthogonal Matching Pursuit

In an underdetermined system,compressive sensing can be used to recover the support vector.Greedy algorithms will recover the support vector indices in an iterative manner.Generalized Orthogonal Matching Pursuit(GOMP)is the generalized form of the Orthogonal Matching Pursuit(OMP)algorithm where a number of indices selected per iteration will be greater than or equal to 1.To recover the support vector of unknown signal‘x’from the compressed measurements,the restricted isometric property should be satisfied as a sufficient condition.Finding the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support recovery.In this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal‘x’using GOMP has been derived.The derived sufficient condition will recover support vectors of P-sparse signal within‘P’iterations.The recovery guarantee for GOMP is less restrictive,and applies to OMP when the number of selection elements equals one.Simulation shows the superior performance of the GOMP algorithm compared with other greedy algorithms.

Based on Compressed Sensing of Orthogonal Matching Pursuit Algorithm Image Recovery

Compressive sensing theory mainly includes the sparsely of signal processing,the structure of the measurement matrix and reconstruction algorithm.Reconstruction algorithm is the core content of CS theory,that is,through the low dimensional sparse signal recovers the original signal accurately.This thesis based on the theory of CS to study further on seismic data reconstruction algorithm.We select orthogonal matching pursuit algorithm as a base reconstruction algorithm.Then do the specific research for the implementation principle,the structure of the algorithm of AOMP and make the signal simulation at the same time.In view of the OMP algorithm reconstruction speed is slow and the problems need to be a given number of iterations,which developed an improved scheme.We combine the optimized OMP algorithm of constraint the optimal matching of item selection strategy,the backwards gradient projection ideas of adaptive variance step gradient projection method and the original algorithm to improve it.Simulation experiments show that improved OMP algorithm is superior to traditional OMP algorithm of improvement in the reconstruction time and effect under the same condition.This paper introduces CS and most mature compressive sensing algorithm at present orthogonal matching pursuit algorithm.Through the program design realize basic orthogonal matching pursuit algorithms,and design realize basic orthogonal matching pursuit algorithm of one-dimensional,two-dimensional signal processing simulation.

Acoustic sound speed profile inversion based on orthogonal matching pursuit

The estimation of ocean sound speed profiles(SSPs)requires the inversion of an acoustic field using limited observations.Such inverse problems are underdetermined,and require regularization to ensure physically realistic solutions.The empirical orthonormal function(EOF)is capable of a very large compression of the data set.In this paper,the non-linear response of the sound pressure to SSP is linearized using a first order Taylor expansion,and the pressure is expanded in a sparse domain using EOFs.Since the parameters of the inverse model are sparse,compressive sensing(CS)can help solve such underdetermined problems accurately,efficiently,and with enhanced resolution.Here,the orthogonal matching pursuit(OMP)is used to estimate range-independent acoustic SSPs using the simulated acoustic field.The superior resolution of OMP is demonstrated with the SSP data from the South China Sea experiment.By shortening the duration of the training set,the temporal correlation between EOF and test sets is enhanced,and the accuracy of sound velocity inversion is improved.The SSP estimation error versus depth is calculated,and the 99%confidence interval of error is within±0.6 m/s.The 82%of mean absolute error(MAE)is less than 1 m/s.It is shown that SSPs can be well estimated using OMP.

Coherence-based performance analysis of the generalized orthogonal matching pursuit algorithm

The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.

基于改进OMP算法的多目标高速机动检测方法

针对多目标高速机动检测问题,提出了一种基于改进正交匹配追踪(OMP)算法的多目标检测方法。根据高速机动目标运动特性建立信号模型;利用改进OMP算法对脉冲压缩后的回波信号进行运动参数估计;构建相位补偿函数对距离徙动和多普勒徙动进行校正;通过快速傅里叶变换(FFT)完成相参积累,实现对多目标的检测。改进算法适用于多目标高速机动检测场景,可有效避免盲速旁瓣现象及信号交叉项的影响,且具有参数估计精度高和抗噪声能力强等优点。仿真实验验证了改进算法的有效性与可靠性。

自适应STWF与改进OMP的滚动轴承微弱故障诊断方法

针对工业环境中随机冲击干扰下滚动轴承微弱故障特征提取难题,提出一种基于自适应短时维纳滤波(Adaptive Short Time Wiener Filtering,ASTWF)和改进正交匹配追踪(Orthogonal Matching Pursuit,OMP)的滚动轴承故障特征提取方法。该方法首先采用包络峭度和随余比(Random Shocks and Margin Ratio,RMR)作为联合判据,界定窗长界限并自适应确定STWF最优窗长参数,进而将随机冲击干扰从测试信号中分离出来;然后,利用立方包络自相关谱估计信号中周期频率,构造周期原子库,降低匹配原子冗余度;最后,利用相似性理论优化匹配追踪迭代终止条件,并结合周期原子库,实现弱故障冲击特征快速、准确提取。根据仿真信号和通过变速箱下线检测所得工程数据,可验证所提出方法可有效识别随机冲击干扰下的滚动轴承微弱故障特征。对比最小熵形态反卷积(Minimum Entropy Morphological Deconvolution,MEMD)方法对于随机冲击干扰下滚动轴承微弱故障特征提取效果,发现所提出方法具有更好的故障特征提取能力;与经典OMP方法相比,所提出改进OMP方法信号重构速度提升66%。

基于DFT-SWOMP的OFDM系统信道估计方法

基于压缩感知的OFDM信道估计方案中,分段弱正交匹配追踪(SWOMP)算法具有不需要预知信道稀疏度的优点,但其信道估计精度受输入的门限参数和迭代次数的影响较大。针对这一问题,提出一种基于DFT-LS算法的门限自适应的SWOMP算法改进方案。考虑到在OFDM系统中,保护间隔长度外的信道时域响应都可以视为噪声,因此该方案的核心思想是利用DFT-LS算法预估出噪声水平,并用此预估值来动态设置SWOMP算法的门限参数。同时,该方案还使用DFT-LS算法预估出的信道频域响应作为SWOMP算法的迭代停止条件。仿真结果表明,这种SWOMP算法的改进方案可以有效地估计出信道参数,并且相比SWOMP算法,其估计结果的MSE值在不同信噪比下都有不同程度的提升。

太赫兹大规模MIMO系统DSP-OMP混合预编码设计

太赫兹具有频谱资源丰富、传输速率高等优势,但其波束分裂效应会造成可达速率及阵列增益损失严重。针对太赫兹大规模多输入多输出系统波束分裂问题,提出一种基于时延相移正交匹配追踪混合预编码方案。通过在射频链和传统移相器网络之间引入一个时延网络缓解波束分裂,结合正交匹配追踪算法降低角度估计带来的计算复杂度。仿真结果表明,所提方案能够有效补偿阵列增益损失,相比传统算法呈现较好的可达速率性能。

基于FFT-OMP-DAMAS波束形成方法的汽车前围板隔声薄弱部位识别

为实现汽车前围板隔声薄弱部位的准确识别,文章提出了基于快速傅里叶变换(Fast Fourier Transform,FFT)和正交匹配追踪(Orthogonal Matching Pursuit,OMP)的反卷积(Deconvolution Approach for the Mapping of Acoustic Sources,DAMAS)波束形成方法(FFT-OMP-DAMAS)。该方法基于声源稀疏分布假设,利用正交匹配追踪思想求解反卷积问题,并进一步结合傅里叶变换和点扩散函数空间转移不变假设降低计算维度。在混响室-消声室内,分别利用延迟求和方法,DAMAS方法和FFT-OMP-DAMAS方法进行了某汽车前围板隔声薄弱部位识别试验,结果表明:FFTOMP-DAMAS方法能够有效抑制旁瓣和伪源,有效缩减主瓣宽度,从而准确识别汽车前围板隔声薄弱部位,且相较于传统的DAMAS方法,文中提出的FFT-OMP-DAMAS方法能获得更清晰的成像结果,计算效率有了明显提高。

GS-orthogonalization OMP method for space target detection via bistatic space-based radar

A space-based bistatic radar system composed of two space-based radars as the transmitter and the receiver respectively has a wider surveillance region and a better early warning capability for high-speed targets,and it can detect focused space targets more flexibly than the monostatic radar system or the ground-based radar system.However,the target echo signal is more difficult to process due to the high-speed motion of both space-based radars and space targets.To be specific,it will encounter the problems of Range Cell Migration(RCM)and Doppler Frequency Migration(DFM),which degrade the long-time coherent integration performance for target detection and localization inevitably.To solve this problem,a novel target detection method based on an improved Gram Schmidt(GS)-orthogonalization Orthogonal Matching Pursuit(OMP)algorithm is proposed in this paper.First,the echo model for bistatic space-based radar is constructed and the conditions for RCM and DFM are analyzed.Then,the proposed GS-orthogonalization OMP method is applied to estimate the equivalent motion parameters of space targets.Thereafter,the RCM and DFM are corrected by the compensation function correlated with the estimated motion parameters.Finally,coherent integration can be achieved by performing the Fast Fourier Transform(FFT)operation along the slow time direction on compensated echo signal.Numerical simulations and real raw data results validate that the proposed GS-orthogonalization OMP algorithm achieves better motion parameter estimation performance and higher detection probability for space targets detection.

基于分布式压缩感知的改进SOMP信道估计算法

针对多径信道联合稀疏模型,基于分布式压缩感知理论提出了一种适用于正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)通信系统的改进同时正交匹配追踪(Simultaneous Orthogonal Matching Pursuit,SOMP)信道估计算法。该算法首先联合多个符号利用比较残差和的方式,在每次迭代中估计各符号信道响应公共支撑集与相应元素直到公共支撑集估计结束,然后对各符号信道响应非公共支撑集单独进行估计,最终得到多个符号的信道响应估计值。仿真结果表明,改进的SOMP算法在JSM-2模型下性能与传统的SOMP算法相近,在JSM-1模型下性能优于传统的SOMP算法与OMP算法。

基于3D-OMP算法的SAR动目标成像方法

针对稀疏场景下的SAR动目标成像问题展开研究,提出一种基于三维正交匹配追踪(3D-OMP)算法的稀疏成像方法。首先对成像区域进行网格划分,然后以运动目标的二维速度作为动态参数构建三维稀疏字典矩阵,即参数化稀疏表征。在算法迭代过程中,通过计算回波数据矩阵与三维稀疏字典矩阵各层之间的相关度筛选出信号的支撑集。最后利用最小二乘准则,计算出支撑集下目标场景的稀疏表征系数。该3DOMP算法是经典OMP算法的改进与拓展,因此继承了OMP算法计算复杂度低、信号稀疏特征增强明显的优势,同时具备了重构SAR动目标图像的能力。仿真实验结果验证了该SAR动目标成像方法的有效性。

THE EXACT RECOVERY OF SPARSE SIGNALS VIA ORTHOGONAL MATCHING PURSUIT

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.

A modified OMP method for multi-orbit three dimensional ISAR imaging of the space target

The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is proposed based on mutliorbit observation data and an improved orthogonal matching pursuit(OMP)algorithm.Firstly,the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension.Then,an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data.Finally,scattering centers can be reconstructed with specific three dimensional locations.Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.

QBFO-BOMP Based Channel Estimation Algorithm for mmWave Massive MIMO Systems

At present,the traditional channel estimation algorithms have the disadvantages of over-reliance on initial conditions and high complexity.The bacterial foraging optimization(BFO)-based algorithm has been applied in wireless communication and signal processing because of its simple operation and strong self-organization ability.But the BFO-based algorithm is easy to fall into local optimum.Therefore,this paper proposes the quantum bacterial foraging optimization(QBFO)-binary orthogonal matching pursuit(BOMP)channel estimation algorithm to the problem of local optimization.Firstly,the binary matrix is constructed according to whether atoms are selected or not.And the support set of the sparse signal is recovered according to the BOMP-based algorithm.Then,the QBFO-based algorithm is used to obtain the estimated channel matrix.The optimization function of the least squares method is taken as the fitness function.Based on the communication between the quantum bacteria and the fitness function value,chemotaxis,reproduction and dispersion operations are carried out to update the bacteria position.Simulation results showthat compared with other algorithms,the estimationmechanism based onQBFOBOMP algorithm can effectively improve the channel estimation performance of millimeter wave(mmWave)massive multiple input multiple output(MIMO)systems.Meanwhile,the analysis of the time ratio shows that the quantization of the bacteria does not significantly increase the complexity.

基于压缩感知的缺失机械振动信号重构新方法

针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。

基于改进广义正交匹配追踪的低地球轨道卫星MIMO-OTFS系统的信道估计方法

针对基于多输入多输出(MIMO)技术和正交时频空间(OTFS)调制的低地球轨道卫星系统的复杂性带来的信道估计困难问题,提出一种基于改进广义正交匹配追踪(GOMP)的信道估计方法。根据单输入单输出(SISO)-OTFS系统的输入输出关系和低地球轨道卫星信道的传播特性,建立一种基于MIMO-OTFS的低地球轨道卫星信道模型,并将系统的信道估计问题转化为稀疏信号的恢复问题。考虑到传统的GOMP算法存在对稀疏度的过度依赖和对稀疏信号的重构精度差等问题,所提方法结合了分段弱正交匹配追踪(SWOMP)的弱选择思想和广义Jaccard系数的相似性准则,以快速准确地重建稀疏信号。仿真结果表明,当天线数为16且导频开销比为0.5时,与正交匹配追踪(OMP)算法相比,所提方法的归一化均方误差(NMSE)降低了约2.5 dB,误码率(BER)降低了约5 dB。

Robustness of orthogonal matching pursuit under restricted isometry property

Orthogonal matching pursuit （OMP） algorithm is an efficient method for the recovery of a sparse signal in compressed sensing, due to its ease implementation and low complexity. In this paper, the robustness of the OMP algorithm under the restricted isometry property （RIP） is presented. It is shown that 5K＋V/KOK,1 〈 1 is sufficient for the OMP algorithm to recover exactly the support of arbitrary /（-sparse signal if its nonzero components are large enough for both 12 bounded and lz~ bounded noises.

Analysis of orthogonal multi-matching pursuit under restricted isometry property

Orthogonal multi-matching pursuit（OMMP）is a natural extension of orthogonal matching pursuit（OMP）in the sense that N（N≥1）indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property（RIP）is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N＋1＋√K/NθKN-N＋1,N〈1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.

A new result on recovery sparse signals using orthogonal matching pursuit

Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we obtained a new number of iterations required for the OMP algorithm to perform exact recovery of sparse signals,which improves significantly upon the latest results as we know.